Abstract
assumption, it may happen that there is a large distortion between the two distances, resulting in some unusual rates of convergence for the squared L2-risk, as noticed by Baraud. We explain this phenomenon and then show that the use of the Hellinger distance instead of the L2-distance allows us to recover the usual rates and to carry out model selection in great generality. An extension to the L2risk is given under a boundedness assumption similar to that given by Wegkamp and by Yang.
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